# Vectors Lab Essay

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Jordan. Physics IB, 16/10/05 IB Lab - The Addition and Resolution Of Vectors: The Force Table Aim: To investigate the relationships and accuracies between the three various methods (graphical, analytical, and experimental) for calculating vector addition and vector resolution. Hypothesis: Both the graphical and mathematical methods should not only have the same results to each other, but if accuracies are avoided, the results should correspond to the experimental force table method. Although there can be many ways to calculate vector addition, in the end they all are relatively similar and since trying to achieve the exact same objective, should have identical answers. I would hypothesize that the results from the graphical method will at times differ from the analytical (mathematical) method since accuracy is limited greatly in the graphical way whereas by the mathematical method it is as exact as it can get. There are three equivalent graphical methods for adding two vectors, the first the parallelogram method, the other is the tail-to-head method, and the last is by using vector components. There is also the mathematical method which requires no scaled diagram (perhaps a small sketch) but does require the manipulation of several mathematical laws and formulas, such as being able to use Pythagoreans Theorem, sine, cosine and tangent, and the sine and cosine laws. Pythagoreans Theorem: a2 + b2 = c2 where c is the hypotenuse while a and b are the sides of the triangle. Sine, Cosine, Tangent: For any unknown angle Ø within a right-angled triangle, sin Ø = opposite/hypotenuse, cos Ø = adjacent/hypotenuse and tan Ø = opposite/adjacent sides. Sine Law: For any triangle, sin(a)/a = sin(b)/b = sin(g)/c Cosine Law: For a triangle with sides of length a, b and c, and angle θ opposite the side of length c, the cosine law says that, c2 = a2 + b2